On 1 Apr., 17:05, William Hughes <wpihug...@gmail.com> wrote:> On Mar 27, 8:55 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > Matheology § 233>> > The set of all termination decimals is a subset of Q. If the set of> > all terminating decimals of the unit interval is arranged as set of> > all terminating paths of the decimal tree,>> It is, of course, impossible to write this out> (there number of terminating decimals is infinite).

Nevertheless Cantor has given a finite formula to construct the listof all rationals between 0 and 1. From that formula we can find everyentry and the anti-diagonal up to every digit d_n. From that we caneasily prove that for every FIS d_1, d_2, ..., d_n of d there areinfinitely many rationals with the same FISs. For every finite numbern - and there are no other lines than such enumerated with a finitenumber!